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A discrete Homotopy Theory for Graphs and its Relation to Subspace Arrangements
Algebra & Discrete Mathematics| Speaker: | Helene Barcelo, Arizona State University |
| Location: | 693 Kerr |
| Start time: | Fri, Nov 19 2004, 12:10PM |
Description
We present the construction of a bigraded family of groups (A-groups)
associated to graphs, and simplicial complexes.
This theory resembles
classical homotopy theory of spaces and
satisfies many of the same properties. However, it depends heavily on
the combinatorial structure of the
objects; for instance, it is not invariant under subdivisions of
simplicial complexes.
We will discuss the connections between the A-groups associated to the
order complex of
the Boolean lattice and the classical homotopy groups of the complement of the
k-equal arrangements.